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Example grid for a cross-figure puzzle with some answers filled in. A cross-figure (also variously called cross number puzzle or figure logic) is a puzzle similar to a crossword in structure, but with entries that consist of numbers rather than words, where individual digits are entered in the blank cells.
Thus a single line can be drawn connecting all nine dots—which would appear as three lines in parallel on the paper, when flattened out. [18] It is also possible to fold the paper flat, or to cut the paper into pieces and rearrange it, in such a way that the nine dots lie on a single line in the plane (see fold-and-cut theorem). [17]
Add the clues together, plus 1 for each "space" in between. For example, if the clue is 6 2 3, this step produces the sum 6 + 1 + 2 + 1 + 3 = 13. Subtract this number from the total available in the row (usually the width or height of the puzzle). For example, if the clue in step 1 is in a row 15 cells wide, the difference is 15 - 13 = 2.
Dots and boxes is a pencil-and-paper game for two players (sometimes more). It was first published in the 19th century by French mathematician Édouard Lucas, who called it la pipopipette. [1] It has gone by many other names, [2] including dots and dashes, game of dots, [3] dot to dot grid, [4] boxes, [5] and pigs in a pen. [6]
With the bent hypotenuse, the first figure actually occupies a combined 32 units, while the second figure occupies 33, including the "missing" square. The amount of bending is approximately 1 / 28 unit (1.245364267°), which is difficult to see on the diagram of the puzzle, and was illustrated as a graphic. Note the grid point where the ...
Quincunx antialiasing samples scenes at the corners and centers of each pixel. These five sample points, in the shape of a quincunx, are combined to produce each displayed pixel. However, samples at the corner points are shared with adjacent pixels, so the number of samples needed is only twice the number of displayed pixels. [3]
Hybrid grid can also be used. Hybrid grids are those in which mixture of triangular and quadrilateral elements are used to construct grids. In three dimension combination of tetrahedral and hexahedral elements results in hybrid grid. Example of hybrid grid is shown in Figure 5.
Hexagonal paper shows regular hexagons instead of squares. These can be used to map geometric tiled or tesselated designs among other uses. Isometric graph paper or 3D graph paper is a triangular graph paper which uses a series of three guidelines forming a 60° grid of small triangles. The triangles are arranged in groups of six to make hexagons.